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Naive Multi-Scale Optimization Algorithm for bound-constrained black-box global optimization problems

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Welcome to NMSO.

This page hosts the MATLAB code for the Naive Multi-Scale Optimization (NMSO) algorithm to appear in, "A Naive Multi-Scale Algorithm for Global Optimization Problems", by Abdullah Al-Dujaili and S. Suresh.

This algorithm has secured the third place out of 28 algorithms in the BBComp competition in GECCO'15. For more details, please refer to this.

Quick Demo

Fire MATLAB and run the following:


This will walk you through a short demo of NMSO in action optimizing a function in 1-D and 2-D. You may want to toy with the algorithm's parameters (e.g., alpha and beta to get a better performance depending on the problem at hand).

How to use NMSO

NMSO has been designed for Black-box Bound-constrained Global Optimization problems. The following would minimize a spherical function whose optimal solution at x=[0.231 0.231] in a 2-D problem space, with the variables being limited to [0,1], using a function evaluation budget of 1000.

func = @(x) sum((x-0.231).^2);
dim = 2;
maxRange = 1;
minRange = 0;
numEvaluations = 1000;
ftarget = 0;
[yBest,xBest]= NMSO(ftarget, func, numEvaluations, dim, maxRange, minRange, 0);


If you write a scientific paper describing research that made use of this code, please cite the following paper:

title = "A Naive multi-scale search algorithm for global optimization problems ",
journal = "Information Sciences ",
volume = "372",
number = "",
pages = "294 - 312",
year = "2016",
note = "",
issn = "0020-0255",
doi = "",
url = "",
author = "Abdullah Al-Dujaili and S. Suresh",
keywords = "Black-box optimization",
keywords = "Global optimization",
keywords = "Derivative-free optimization",
keywords = "Partitioning-based",
keywords = "Optimistic algorithms",
keywords = "Finite-time analysis ",
abstract = "Abstract This paper proposes a multi-scale search algorithm for solving global optimization problems given a finite number of function evaluations. We refer to this algorithm as the Naive Multi-scale Search Optimization (NMSO). \{NMSO\} looks for the optimal solution by optimistically partitioning the search space over multiple scales in a hierarchical fashion. Based on a weak assumption about the function smoothness, we present a theoretical analysis on its finite-time and asymptotic convergence. An empirical assessment of the algorithm has been conducted on the noiseless Black-Box Optimization Benchmarking (BBOB) testbed and compared with the state-of-the-art optimistic as well as stochastic algorithms. Moreover, the efficacy of \{NMSO\} has been validated on the black-box optimization competition within the GECCO’15 conference where it has secured the third place out of twenty-eight participating algorithms. Overall, \{NMSO\} is suitable for problems with limited function evaluations, low-dimensionality search space, and objective functions that are separable or multi-modal. Otherwise, it is comparable with the top performing algorithms. "